scholarly journals Classical KMS condition and Tomita-Takesaki theory

1976 ◽  
Vol 47 (1) ◽  
pp. 95-95
Author(s):  
G. Gallavotti ◽  
M. Pulvirenti
Keyword(s):  
Kms Condition

scholarly journals On the Modular Operator of Mutli-component Regions in Chiral CFT

2021 ◽  
Author(s):  
Stefan Hollands
Keyword(s):  
Field Theory ◽  
Integral Equation ◽  
Hilbert Problem ◽  
Matrix Elements ◽  
New Approach ◽  
Conformal Field ◽  
The Matrix ◽  
Kms Condition ◽  
Modular Operator ◽  
Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

scholarly journals Resolving modular flow: a toolkit for free fermions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Johanna Erdmenger ◽  
Pascal Fries ◽  
Ignacio A. Reyes ◽  
Christian P. Simon
Keyword(s):  
Complex Analysis ◽  
Conformal Symmetry ◽  
Standard Technique ◽  
Analytic Structure ◽  
Point Function ◽  
Free Fermions ◽  
Modular Evolution ◽  
Non Local ◽  
Kms Condition ◽  
New Formula

Abstract Modular flow is a symmetry of the algebra of observables associated to space-time regions. Being closely related to entanglement, it has played a key role in recent connections between information theory, QFT and gravity. However, little is known about its action beyond highly symmetric cases. The key idea of this work is to introduce a new formula for modular flows for free chiral fermions in 1 + 1 dimensions, working directly from the resolvent, a standard technique in complex analysis. We present novel results — not fixed by conformal symmetry — for disjoint regions on the plane, cylinder and torus. Depending on temperature and boundary conditions, these display different behaviour ranging from purely local to non-local in relation to the mixing of operators at spacelike separation. We find the modular two-point function, whose analytic structure is in precise agreement with the KMS condition that governs modular evolution. Our ready-to-use formulae may provide new ingredients to explore the connection between spacetime and entanglement.

THE KMS CONDITION FOR *-ALGEBRAS

1981 ◽  
Vol 373 (1 Fourth Intern) ◽  
pp. 22-27
Author(s):  
J. Alcántara ◽  
D. A. Dubin
Keyword(s):  
Kms Condition

On the equivalence of adiabatic invariance and the KMS-condition

1983 ◽  
Vol 13 (3) ◽  
pp. 409-415 ◽  
Author(s):  
W. Thirring
Keyword(s):  
Adiabatic Invariance ◽  
Kms Condition

scholarly journals Analytic generators and the KMS condition

1983 ◽  
Vol 88 (2) ◽  
pp. 287-287
Author(s):  
Jean De Canni{ère
Keyword(s):  
Kms Condition
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